Stroke Prevention in Atrial Fibrillation (SPAF 3) is a multicenter, NIH funded trial to determine the best and safest way to reduce stroke risk in atrial fibrillation. Based on data from SPAF2, patients with chronic atrial fibrillation will be stratified according to high or low risk of stroke. Patients at low risk of stroke will be treated with one aspirin per day (325mg) and those at high risk of stroke will be randomized to receive either Warfarin in a standard dose to maintain a INR at 2-3 or low Warfarin (1-3mg sufficient to midly elevate the INR to 1.3). Subjects will be following at regular intervals with baseline and regular neurological examinations to determine any evidence of stroke and to determine any complications of therapy.